On the plane-wave cubic vertex

TL;DR

This paper derives exact bosonic Neumann matrices for the cubic vertex in plane-wave light-cone string field theory, using contour integration and ermed Gamma-functions, simplifying previous methods and analyzing their asymptotic behavior.

Contribution

It introduces a simplified derivation of the Neumann matrices expressed via ermed Gamma-functions, extending the flat-space solution to plane-wave backgrounds.

Findings

Explicit expression for the first exponential correction to the Neumann matrices.

Asymptotic analysis of ermed Gamma-functions for large ermed parameter.

Conjecture on higher-order exponential correction terms.

Abstract

The exact bosonic Neumann matrices of the cubic vertex in plane-wave light-cone string field theory are derived using the contour integration techniques developed in our earlier paper. This simplifies the original derivation of the vertex. In particular, the Neumann matrices are written in terms of \mu-deformed Gamma-functions, thus casting them into a form that elegantly generalizes the well-known flat-space solution. The asymptotics of the \mu-deformed Gamma-functions allow one to determine the large-\mu behaviour of the Neumann matrices including exponential corrections. We provide an explicit expression for the first exponential correction and make a conjecture for the subsequent exponential correction terms.